Hi Billie,
you may be conflating 2 questions here- your company name and trading name can be two very different things.
Your company name is what the limited company is registered as and whilst there are restrictions, you have pretty free reign. You could be "Billiehop The best 123456 Limited", however your trading name might be Tesco. So you'd be Billiehop The best 123456 Limited T/As Tesco.
In this scenario you'd be sued (well they'd start with a very strong solicitors letter, but you know what i mean) very quickly by Tesco for using their name, but not for the Ltd Co name.
A lot of people ask about company names without realising what they are actually interested is trademarked/registered name.
Mark's link allows you to check the name of a limited company.
This link will allow you to check if anyone has trademarked the name you like: [can't post a link as i've not been here long enough- but google "UK trademark search"
If a name is trademarked, depending on the class, then that's pretty final.